- #1

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## Main Question or Discussion Point

Hello Everyone!

I want to learn about Fourier series (not Fourier transform), that is approximating a continuous periodic function with something like this ##a_0 \sum_{n=1}^{\infty} (a_n \cos nt + b_n \sin nt)##. I tried some videos and lecture notes that I could find with a google search but those materials were not very helpful. I want to know how we came up with something like that and its applications.

My current knowledge is that I know mathematics up to Calculus I (that is single variable calculus) and just a beginner in Multivariable Calculus and Real Analysis. Please suggest me some books that explains Fourier series approximation for any function in a detailed manner. I think a complete separate book on Fourier Analysis (which google search is giving me) requires some high level knowledge of analytical tools, I need something introductory.

Thank you.

I want to learn about Fourier series (not Fourier transform), that is approximating a continuous periodic function with something like this ##a_0 \sum_{n=1}^{\infty} (a_n \cos nt + b_n \sin nt)##. I tried some videos and lecture notes that I could find with a google search but those materials were not very helpful. I want to know how we came up with something like that and its applications.

My current knowledge is that I know mathematics up to Calculus I (that is single variable calculus) and just a beginner in Multivariable Calculus and Real Analysis. Please suggest me some books that explains Fourier series approximation for any function in a detailed manner. I think a complete separate book on Fourier Analysis (which google search is giving me) requires some high level knowledge of analytical tools, I need something introductory.

Thank you.